A Fast O(N log N) Finite Difference Method for the One-Dimensional Space-Fractional Diffusion Equation

Mathematics

Treena Basu¹ 

[1] Department of Mathematics, Occidental College, Los Angeles, CA 90041, USA; E-Mail

关键词: circulant and toeplitz matrices;    fast finite difference methods;    fast fourier transform;    fractional diffusion equations;   

DOI  :  10.3390/math3041032

来源: mdpi

【 摘 要 】

This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement ofper iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.